Process identification and search for optimal differentiation parameters from major element data. General presentation with emphasis on the fractional crystallization process

Different igneous differentiation processes result in various evolution trends in a certain composition space Rⁿ. Almost every genetic process can be described as a single two-pole mixing process, which leads to a straight evolution line in Rⁿ; or as a series of two-pole mixing processes, which in the general case leads to a broken curved evolution line.When a fundamental two-pole mixing process clearly prevails over one or several secondary processes in the genesis of a volcanic suite, a ‘best’ mixing line in Rⁿ can be computed with due attention to experimental uncertainties. A number of statistical tools are available for testing the data-uncertainties-linear model consistency and for pointing out a few dubious data, or the influence of a few secondary processes.The best mixing line and its associated error volumes serve to quantify the trend, and then can be used to get some ‘best’ estimate (or competitive acceptable estimates) of the mineralogical parameters that control the genetic process.Any mineral assemblage defines a continuous composition family in Rⁿ which can be characterized by its gaussian distance to the best mixing line. In the framework of a fractional crystallization model, that distance serves as a test for accepting or rejecting the mineral assemblage as a likely candidate for representing the crystallizing solid.In favorable situations the minimization procedure used to compute the distance also determines both the mineral proportions in the crystallizing solid and their compositions. In less favorable situations it may leave us with some indeterminacy among a small number of acceptable interpretations.The mixing line calculation and the mineralogical inversion procedure are applied to the classical Kilauea Iki Lava Lake (Hawaii) example, where olivine and chromite crystallization with incomplete solid-liquid separation is shown to be a likely explanation for the observations, along with near-surface iron oxidation as a secondary process.The origin of volcanic rocks from Terceira Island (Azores) is less clear. It is shown that the simultaneous crystallization of olivine, Ti-augite and plagioclase can be retained as an acceptable interpretation for the least differentiated rocks, but that substantial secondary processes are also involved.